Department of Economics. Issn Discussion paper 19/08

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1 Department of Economics Issn Discussion paper 19/08 INFORMATION GATHERING, DELEGATED CONTRACTING AND CORPORATE HIERARCHIES Chongwoo Choe and In-Uck Park 2008 Chongwoo Choe and In-Uck Park A rights reserved. No part of this paper may be reproduced in any form, or stored in a retrieva system, without the prior written permission of the author.

2 Information Gathering, Deegated Contracting and Corporate Hierarchies 1 March 23, 2008 Chongwoo Choe Department of Economics Monash University Emai: Chongwoo.Choe@buseco.monash.edu.au and In-Uck Park Department of Economics University of Bristo Emai: I.park@bristo.ac.uk Pease send a correspondence to: Chongwoo Choe Department of Economics Monash University PO Box 197, Caufied East VIC 3145, Austraia (Phone) +61 (0) (Fax) +61 (0) (Emai) Chongwoo.Choe@buseco.monash.edu.au 1 This project was started during the first author s visit to the University of Pittsburgh and the Research Institute of Capita Formation, Deveopment Bank of Japan, whose warm hospitaity is gratefuy acknowedged. We are thankfu for many hepfu comments from the seminar audience at various institutions. This project was funded by a Discovery Project Grant (DP ) from the Austraian Research Counci. The usua discaimer appies. 1

3 Information Gathering, Deegated Contracting, and Corporate Hierarchies Abstract In a typica corporate hierarchy, the manager is deegated the authority to make strategic decisions, and to contract with other empoyees. We study when such deegation can be optima. In centraization, the owner retains the authority, which fais to motivate the manager to acquire vauabe information, eading to suboptima decisions and inefficient incentive provision to the worker. Beneficia deegation shoud necessariy motivate the manager to acquire information, which is possibe ony when the authority is deegated to the manager. We aso document comparative statics resuts regarding the benefits of deegation and discuss when deegation is more ikey to dominate centraization. JEL Codes: C72, D21, D82, L22. Keywords: Corporate hierarchies, information gathering, deegation, centraization. 1

4 1. Introduction The so-caed separation of ownership and contro (Bere and Means, 1932; Fama and Jensen, 1983) refers to the fact that the nomina owners of corporations - sharehoders - deegate authority to managers. The authority is vested in severa important dimensions for the top managers of corporations. They make strategic decisions that set directions for corporations, empoy subordinates, and contract with externa suppiers. This mutipe dimension of authority is a deciding factor for the organizationa form of corporations. Rather than a set of two-tier hierarchies in which owners are at the top of each two-tier hierarchy, modern corporations are often organized as mutitier hierarchies. 1 Chander (1977, 1990) attributes such a transformation of famiy-oriented persona capitaism to manageria capitaism in the US to a sharp increase in demand for, and suppy of professiona, quaified managers as corporations become arger with increasingy sophisticated operations. The resuting modern business enterprise, according to Chander, is an organization with many distinct operating units that are managed by a hierarchy of professiona, saaried executives. In such organizations, sharehoders hire top managers - through boards - and managers, in turn, hire subordinates or contract with externa suppiers. Why are such muti-tier hierarchies, rather than mutipe two-tier hierarchies, often the norm? Why are managers, instead of other stakehoders, at the center of the muti-tier hierarchy? This study attempts to provide answers to these questions from an incentive perspective. A typica expanation for deegation in corporations is based on managers expertise and the ensuing benefits of speciaization. Jensen and Murphy (1990, p. 251) put it apty: Managers often have better information than sharehoders and boards in identifying investment opportunities and assessing the profitabiity of potentia projects; indeed, the expectation that managers wi make superior investment decisions expains why sharehoders reinquish decision rights over their assets by purchasing common stocks. Underying this expanation is the assumption that communicating managers information is costy, or that sharehoders or boards do not have necessary expertise to process the information for decision-making even if communicating the 1 Separation of ownership and contro in this sense, athough not universay the case, is most prevaent in the Ango-American system of corporate governance. See La Porta, Lopez-De-Sianes and Sheifer (1999). 2

5 information is costess. 2 For, otherwise, sharehoders or boards wi be abe to make decisions based on the information that managers have, which is the centra insight from the reveation principe. We take Jensen and Murphy s expanation as a starting point, but go a step further by assuming that managers need to incur private costs to acquire and process information. The incentive probem becomes reativey easier without such costs. Our basic mode is thus embedded in an environment where managers can, at some costs, acquire information necessary for investment decisions, which cannot be used by sharehoders in designing incentive contracts for managers. Severa authors have resorted to such contractua incompeteness either impicity or expicity to expain why a muti-tier hierarchy with deegation can be superior to a centraized mechanism. In the context of genera reveation mechanisms, Meumad, Mookherjee and Reichestein (1995) show that the outcome of an optima reveation mechanism can be achieved using decentraized contracts and proper sequencing of the contracts. Thus their main point is that, when various contracting costs such as those of communicating information necessary for the reveation mechanism are taken into account, there may be benefits to deegation. Laffont and Martimort (1998) show that deegation can dominate centraized contracts when the possibiity of cousion down the hierarchy is combined with imits on communication. The imits on communication, according to these authors, require the centraized contracts be anonymous, and different agents be treated symmetricay. This faciitates cousion. With decentraization, such a probem disappears. The main esson from these studies is that, to have hierarchica decentraization emerge endogenousy as an optima organizationa form, there must be imits to using centraized reveation mechanisms. Our paper is simiar in spirit to the above studies, but has more concrete objectives. Specificay we describe what we beieve is a reaistic, but tractabe mode of a corporate hierarchy, and show when and why putting managers at the center of the muti-tier hierarchy can benefit sharehoders. The main point of this paper can be expained using a simpe scenario. Consider a firm that consists of three parties, whom we ca the owner, the manager and the worker. The firm has two investment projects, for which 2 The benefits of hierarchies facing the costs of communicating and processing information have been put forward by Arrow (1974) and Wiiamson (1983) among many others. 3

6 the owner provides necessary funds. The manager can acquire private information at some costs, which can be used in choosing a right project to undertake. The worker can exert effort that can increase the ikeihood that the chosen project is successfu. Neither the manager s information nor the worker s effort can be used for contracting purpose. In a centraized mechanism, the owner has the authority to choose a project based on the manager s report, and design contracts for both agents based on the return from the chosen project. Athough the manager s information cannot be used directy for contracting purpose, it can be used indirecty through the project choice. In a hierarchica mechanism, authority is deegated to the agent in the midde of the three-tier contracting reationship: the owner designs a contract for the agent in the midde, who chooses a project and designs a contract for the other agent. If the manager is deegated authority, he makes a project choice based on his own information. If the worker is deegated authority, he soicits the manager s information to make a project choice. Our main point is that, for a hierarchica mechanism to dominate centraized contracting, authority shoud necessariy be deegated to the manager, not the worker. The intuition is as foows. In a centraized mechanism, the owner needs to contro both the manager s incentives for information gathering and truthfu report, and the worker s incentives for optima effort. The manager s information is vauabe for project choice and subsequent contract design for the worker. The worker s contract in turn affects the return from the chosen project, based on which the manager is paid. Knowing this, the manager has an incentive to manipuate his information if it is expected to increase the worker s effort eve via his contract, which may not be optima for the owner. This makes the manager s incentive compatibiity constraints more stringent than those in the standard principa-agent mode. As a resut, it is too costy for the owner to motivate the manager to gather information and the centraized mechanism fais to induce the manager to gather information. The resuting project choice is suboptima and the worker s contract fais to provide efficient incentives to the worker. Deegating authority to the worker suffers from simiar probems since the worker has to soicit the manager s information for project choice. If authority is deegated to the manager, however, the owner can disentange the interocking incentives. Deegation effectivey makes the manager a 4

7 residua caimant in the subcontracting stage with the worker. Therefore the deegated contracting authority motivates the manager to design an efficient contract for the worker, which is possibe if the manager gathers information and uses it for an optima project choice. 3 Thus the decision-making authority and the deegated contracting authority are compementary. Of course the efficiency benefits of deegation do not automaticay fow back to the owner. If the manager enjoys too much rent as a resut of deegation, then the owner may be better off with centraization. We show that deegation is more ikey to benefit the owner as the manager s cost of information gathering becomes smaer, the manager s information becomes more vauabe, and the worker s cost of effort becomes arger. Other studies on deegation in a hierarchy incude, among others, Baron and Besanko (1992), Gibert and Riordan (1995), McAfee and McMian (1995), Baiga and Sjöström (1998), Macho-Stader and Pérez-Castrio (1998), Mookherjee and Reichestein (2001), Faure-Grimaud, Laffont and Martimort (2003), and Mookherjee and Tsumagari (2004). Baron and Besanko (1992), and Gibert and Riordan (1995) estabish equivaence between centraized and decentraized mechanisms when risk-neutra agents provide compementary inputs to production. McAfee and McMian (1995) consider a three-tier hierarchy subject to imited iabiity constraints, showing osses invoved in a three-tier hierarchy reative to centraized contracting. Equivaence of a decentraized mechanism and a centraized mechanism subject to the possibiity of side-contracting is estabished in a mora hazard environment by Baiga and Sjöström (1998), and Macho-Stader and Pérez- Castrio (1998), in an environment with additiona coordination probems by Mookherjee and Reichestein (2001), and in a principa-supervisor-agent setup by Faure-Grimaud, Laffont and Martimort (2003). 4 An additiona con- 3 In a simiar vein but in a costy verification environment, Choe (1998) shows that the contract designed by the informed party can reduce the verification cost compared to the one designed by the uninformed party. The reason is that the informed party, in an attempt to maximize the vaue of his residua caim, designs the contract to give himsef truth-teing incentives. 4 The equivaence resut can be aso shown in our mode. Suppose side-contracting between the manager and the worker is possibe under centraization. Then the owner can impement the equiibrium outcome from manager deegation by offering the manager the same contract that she woud offer under manager deegation, and the nu contract to the worker. Since the worker s effort is essentia, the manager wi then offer the worker a side-contract that is exacty the same as the worker s contract under manager deegation. 5

8 cusion of Baiga and Sjöström (1998) reates to the pattern of deegation: the agent with superior information is more ikey to be deegated. Mookherjee and Tsumagari (2004) consider a genera adverse seection mode to show that hierarchica deegation is in genera stricty dominated by centraization subject to cousion due to doube marginaization of rents. 5 Whie not directy concerned with deegation, Itoh (1992, 1993) studies a mutipe-agent mora hazard environment to show when the principa can benefit by aowing coaition of agents, when agents can monitor each other. With the equivaence resut described above, his findings can be regarded as supportive of deegation over centraization when agents have informationa advantages over the principa. Our work differs from, but compements these and afore-mentioned studies on hierarchy at east in two important ways. In our mode, the manager is not endowed with private information. Rather, he needs to incur private costs to acquire information. Because of this information acquisition, there are benefits from deegating authority to the manager. In the above studies on hierarchy, there is no a priori reason why a particuar agent shoud be at the center of the muti-tier hierarchy. 6 It coud be any of the agents suppying inputs. In our mode, deegation can benefit the owner ony when the manager, not the worker, assumes the roe of the deegated agent. Thus the benefits of deegation come from circumventing the irreconciabe conficts between the information hoder and the decision maker, which may arise under centraization, preventing a certain outcome from being impementabe. Second and reated, the manageria input and the worker s input are quite distinct. We beieve that the manager s information acquisition and subsequent decision making are what distinguish manageria inputs from those of other empoyees in corporations. 7 Roughy speaking, the manager s decision 5 The main difference between Laffont and Martimort (1998) and Mookherjee and Tsumagari (2004) is that, in the former, the cost types are binary and the bargaining power in the side-contracting at the cousion stage is fixed exogenousy. In Mookherjee and Tsumagari, the bargaining power in the cousion stage is determined endogenousy by the initia contract offered by the principa. Because of this, the principa can contro the outcome from cousion to some extent. Laffont and Martimort were aware of this. They argue that their modeing choice wi ead to the best outcome for the agents, hence the owest bound of what the principa can achieve when cousion is possibe (footnote 9, p. 286). 6 As mentioned above, Baiga and Sjöström (1998) is a notabe exception. 7 In his cassic work, Simon (1960) argues that the most important roe of managers is 6

9 making can be identified with the choice of a particuar distribution of profits, whie other empoyees inputs affect the ikeihood of profit reaization given the chosen distribution. It is in this sense that the manager s main roe can be described as that of direction setting. We thus expect optima incentive schemes for the manager to be quite different from those for other empoyees. Indeed we show that the manager, when deegated authority, can activey affect his own payoff through the choice of project and the design of contract for the worker. Thus incentives and authority are strongy compementary for the party who is deegated authority. For the worker, the scope of such infuence upon his own payoff is imited, as is the case for empoyees ower in the corporate hierarchy: the worker in our paper is paid an efficiency wage under manager deegation. 8 The rest of the paper is organized as foows. Section 2 describes the basic mode. Section 3 studies the centraized mechanism. Section 4 anayzes the case of manager deegation, which is then compared with centraization in Section 5. Section 6 discusses other reevant issues and extends our resuts. Section 7 concudes the paper. The appendix contains the proofs of the resuts that are not centra to the exposition of our main ideas. 2. The Mode There are three parties, whom we ca the owner, the manager and the worker. 9 The owner has two projects, denoted by ψ 1 and ψ 2, whose return has the same support: x > 0 (success) or 0 (faiure). The return is pubicy observabe and can be used for contracting purpose. The manager can privatey observe a signa θ {θ 1, θ 2 } at a monetary cost of c > 0, which we wi ca information gathering. The signa is a perfect predictor of a state which gathering, processing information, and making decisions based on this. According to him, managing is synonymous with decision-making. Case studies by Mintzberg (1973) provide rich supporting evidence for this. Radner (1993) aso treats information processing as the main task of managers, distinct from the roes payed by other empoyees. 8 One coud take this as an incentives-based expanation of why stock options have been the singe most important incentive for CEOs in Ango-American corporations (Murphy, 1999). Whie the use of stock options for non-executive empoyees was aso growing in the ate 1990s (Core and Guay, 2001), the proportion of incentives provided through stock options is ecipsed compared to that for CEOs (The Economist, 2003, p. 9.). 9 We wi use the femae gender pronoun for the owner and the mae gender pronoun for the manager and the worker. 7

10 is a random variabe that assumes θ 1 and θ 2 with probabiities π (0, 1) and 1 π, respectivey. If the manager does not gather information, then he observes nothing and we denote this nu signa by, and the set of a possibe signas by Θ = {θ 1, θ 2, }. The worker privatey chooses work or shirk. The monetary cost of work is and that of shirk is normaized to 0. Given θ i, the success probabiity for ψ 1 (ψ 2, respectivey) is p i (q i, respectivey) if the worker chooses work. 10 If the worker chooses shirk, then the success probabiity is r for either project and state. 11 We assume that a the payers are risk neutra, imited iabiity sets a ower bound of 0 for payments to the manager and the worker, and that reservation utiities for both agents are zero. It then foows that both the manager and the worker find any contract weaky better than the reservation vaue. Hence, we assume in the seque that they wi accept any nonnegative contract. The owner wishes to hire the manager to use his information for project choice, and the worker to exert effort for the chosen project. We consider two organizationa structures that the owner may wish to empoy for this purpose. In a centraized structure, the owner contracts with the manager who makes a report regarding his information, based on which she decides on which project to undertake and what kind of contract to offer to the worker. We assume that the the communication of the manager s information is informa hence unverifiabe. As mentioned in the introduction, some form of transaction costs in communicating oca information to the principa is a necessary condition for effective deegation. We take the simpest form of transaction costs that the manager s information is not verifiabe. The contracts in this case thus depend ony upon the project choice and the fina return. In a deegated structure, the owner contracts with ony one of the agents, who is deegated the authority to choose a project to undertake and to contract directy with the other agent. Either the manager or the worker can be the deegated agent. But the owner never benefits from deegating authority to the worker, which is shown in Section 6.2. Therefore we focus on deegation to the manager except in Section 6.2. The game trees in the two organizationa structures are described more precisey beow. Under centraization, the owner first offers a contract to the 10 Projects are identified with p and q and, states, with the subscripts. 11 Our main quaitative resuts are robust to different success probabiities when the worker shirks, as ong as they are sufficienty sma reative to p i and q i. 8

11 manager that specifies a saary s iρ 0 for each of the contingencies that a project ψ i {ψ 1, ψ 2 } is undertaken and a fina return ρ {x, 0} is produced. The manager accepts the contract, privatey decides whether to gather information, and sends a message m Θ to the owner. Upon receiving m, the owner seects a project to undertake and offers a contract to the worker. The project choice decision is denoted by a mapping C : Θ {ψ 1, ψ 2 }. If the owner seected ψ i {ψ 1, ψ 2 }, then the worker s contract specifies a wage w iρ 0 for each possibe return ρ {x, 0}. The worker accepts the contract and decides on his action. Finay, the return ρ is reaized, the manager and the worker are paid, and the owner keeps the remainder, ρ s iρ w iρ for i = 1, 2. Under deegation, the owner offers a contract to the manager that specifies a saary σ ρ 0 contingent ony on the fina return ρ. That it may not depend on the project choice is for expositiona convenience. Reaxing this assumption ony reinforces our main insight because it woud enhance the performance of the deegated structure for the owner. 12 The manager accepts it, privatey decides whether to gather information and seects a project, and then offers a contract to the worker. If the manager chose ψ i {ψ 1, ψ 2 }, then the worker s contract specifies a wage ω iρ 0 for each ρ {x, 0}. The worker accepts and decides his action. Finay the return ρ is reaized and payments are made: the owner retains ρ σ ρ, the manager σ ρ ω iρ, and the worker gets ω iρ for i = 1, 2. Figure 1 shows the time-ine for the two organizationa structures. Figure 1 goes about here. The payers objectives are to maximize their respective expected payoffs. Since the worker is risk-neutra, the optima contract to induce shirk from the worker in either organizationa structure is 0 regardess of ρ, and that to induce work is a positive wage ony when ρ = x such that the increment in expected wage from work is, the cost of work. In the seque we take this observation granted and denote the wage contract by w i or ω i as shorthand for w ix and ω ix, respectivey. Simiary, we can simpify the manager s contract under centraization to s i0 = 0 and denote s ix 0 by s i for i = 1, We beieve that it aso carries some reaism. When the owner deegates the operation of the firm to the manager, she woud be interested in the fina performance but not in the detais of operation. 9

12 The described structure of the game is common knowedge. We anayze and compare the sequentia equiibrium between the two structures. An outcome refers to a specification of the manager s action, project choice and the worker s action for each state. Define p i p i r, q i q i r, i = 1, 2. These are improvements in success probabiities due to the worker s contribution. We maintain the foowing assumptions. Assumption 1: πp 1 + (1 π)p 2 > πq 1 + (1 π)q 2. Assumption 2: p 1 > p 2 > r, q 2 > q 1 > r, p 1 > x > q 2. Assumption 1 states that the two projects are asymmetric under the prior beief. That is, if the owner has to make a project choice without the manager s information, then she woud prefer ψ 1 to ψ 2 provided that the worker is induced to work. It is intended to resove a tie-breaking situation. Assumption 2 impies that an optima project choice is necessariy statedependent, and that the worker s input is vauabe ony when ψ 1 is chosen in θ 1. These are minima assumptions that make the incentive probems for both agents non-trivia. To see this, suppose that the worker s input is vauabe in both projects if they are optimay chosen, i.e., p 1 > x and q 2 > x. Then the manager s information is vauabe ony for project choice, but not for incentive provision to the worker. In this case, the owner can provide separate incentives to the manager and the worker, thereby impementing the desired outcome through centraization. Therefore deegation and the accompanied interocking incentives do not have much bite. In Section 6.3, we show this formay by demonstrating that deegation is never optima if p 1 > x and q 2 > x. 3. Centraization Under centraization, the owner designs contracts for both agents. Suppose that the manager gathers information given the contract (s 1, s 2 ). Given that the contract satisfies the manager s incentive compatibiity (IC), the manager reports the signa truthfuy. There are four possibe cases of project choice based on the manager s report: (i) C(θ i ) = ψ 1 for i = 1, 2; (ii) C(θ i ) = ψ 2 for i = 1, 2; (iii) C(θ i ) = ψ j for i j; (iv) C(θ i ) = ψ i for 10

13 i = 1, 2. Since the contract that induces the manager to gather information is costy for the owner, if the manager gathers information in equiibrium, the information shoud be used. There is no point for the owner to know the state if she were to induce the worker to shirk in both states. Thus if the manager gathers information, the worker shoud be induced to work in at east one of the two states. Moreover, Assumption 2 impies that the worker s effort is vauabe ony when ψ 1 is chosen in θ 1. In a the other cases, the owner is better off by inducing shirk from the worker since the payment to induce work is nonnegative. Therefore if the manager gathers information in equiibrium, the ony outcome that the owner woud want to impement invoves the worker working ony when ψ 1 is chosen in θ 1. We show beow that the owner cannot impement this outcome. Suppose that the owner offers the worker w 0 to induce work in θ 1, and w = 0 to induce shirk in θ 2. Based on the discussions above, we need to ook at ony two possibe cases of project choice where ψ 1 is chosen in θ 1. Consider first the case where C(θ i ) = ψ 1 for i = 1, 2. Then the manager s IC requires p 1 s 1 rs 1 p 2 s 1, where the first inequaity concerns θ 1 and the second inequaity, θ 2. But this is impossibe since p 2 > r. The next case has C(θ i ) = ψ i for i = 1, 2. The manager s IC in this case is p 1 s 1 rs 2 p 2 s 1, which impies s 2 p 2 r s 1 > s 1. Then, in θ 2, the owner is better off choosing ψ 1 rather than ψ 2. It is because the expected payment when ψ 1 is chosen is rs 1, which is smaer than rs 2, the expected payment when ψ 2 is chosen. 13 In sum, there cannot be an equiibrium in which the manager gathers information and the worker works ony when ψ 1 is chosen in θ 1. Consequenty the owner does not benefit from the manager s information and, therefore, woud not induce the manager to gather information. The ogic behind the above resut is as foows. Under centraization, the owner needs to contro both the manager s incentives for information gathering and truthfu report, and the worker s incentives. The manager s information is vauabe for project choice and subsequent contract design for the worker. If the margina vaue of the worker s input is negative for a project seected based on the manager s report, then an optima contract shoud induce the worker to shirk. The optima shirk from the worker, however, reduces the probabiity that the manager wi be paid. Thus the manager has an incentive to make an untruthfu report if it is expected to induce work 13 Reca that, in θ 2, the owner offers the worker w = 0 to induce shirk. 11

14 from the worker even if it eads to a suboptima project choice at the cost to the owner. Eiciting truthfu reports from the manager then requires the owner to reward the manager more when his report eads to optima shirk from the worker (s 2 > s 1 in the second case above). This makes it too costy for the owner to motivate the manager to gather information. Summarizing the discussions so far, we have Proposition 1: In no equiibrium under centraization, the manager gathers information. There are two reasons for the above impossibiity resut. First, the timing of contracting under centraization is such that the owner designs the worker s contract after earning the manager s report. Since the worker s action affects the manager s expected payoff, the manager wi then have incentives to make untruthfu reports, if necessary, to increase his expected payoff. The resuting stringent incentive constraints for the manager eiminate the benefits of the manager s information for the owner. Therefore, if the owner can commit to the worker s contract that depends ony on the return from the project before receiving the report from the manager and making a project choice, then she can motivate the manager to gather information. However this does not necessariy benefit the owner compared to when she can aso use project choice for contracting purpose. This is discussed in Section 6.1. Second, under centraization, the owner has to design contracts for both agents to contro their respective incentives. As we wi show in the next section, deegation of authority to the manager aows the owner to disentange the incentives of the two agents. It reieves the owner from the onus of project choice and contract design for the worker. The owner offers a contract ony to the manager to provide the incentives for information gathering. The manager in turn uses his information for project choice, based on which to contro the worker s incentives. In any equiibrium under centraization, therefore, the owner does not make a positive payment to the manager who does not gather information. The owner cannot distinguish between the states, hence induces the same action from the worker. If it is optima for her to induce shirk from the worker, then the owner does not use the inputs from either agent. We ca this proprietorship. The owner s expected payoff under proprietorship is 12

15 Z P rx. [1] If the owner induces the worker to work under centraization, then project choice matters. If she chooses ψ 1, then she has to pay the worker in case of success, resuting in the worker s expected payoff of The owner s expected payoff is then π p 1 +(1 π) p 2 r π p 1 +(1 π) p 2. ( ) Z C (πp 1 + (1 π)p 2 ) x. [2] π p 1 + (1 π) p 2 If she chooses ψ 2, then she pays the worker expected payoff of (πq 1 + (1 π)q 2 )(x Z C due to Assumption 1. This eads to π q 1 +(1 π) q 2 and obtains the π q 1 +(1 π) q 2 ), which is smaer than Proposition 2: In the equiibrium under centraization, the owner offers a nu contract to the manager. If Z C > Z P, then the owner chooses ψ 1 and induces the worker to work by offering w 1 = π p 1 +(1 π) p 2 in case of success. If the inequaity is reversed, then the owner chooses proprietorship. 4. Manager Deegation The owner continues to design a contract for the manager, who is now deegated the authority to seect a project and design a contract for the worker. Since our main focus is when deegation can benefit the owner, deegation shoud necessariy impement the outcome that is not possibe to impement under centraization. More precisey, it is easy to see that deegation does not benefit the owner if it cannot motivate the manager to gather information. Proposition 3: Suppose the deegated manager does not gather information. Then, the owner can induce the same outcome under centraization at the same or a ower cost. Proof: Suppose the deegated manager does not gather information. Then he either chooses ψ 1 and induces work by offering ω 1 = π p 1 +(1 π) p 2, or chooses either project and induces shirk by offering ω 1 = ω 2 = 0. In either 13

16 case, the owner can induce the same outcome centray by offering the manager s 1 = s 2 = 0 and repicating the deegated manager s decisions in project choice and contracting with the worker. In ight of Proposition 3, we focus on the outcomes in which the deegated manager gathers information in equiibrium. Again, there is no point for him to gather information if he were to induce shirk from the worker in both states. In addition, since the saary to the manager is at most x, he has no incentive to induce work from the worker in state θ 2 due to Assumption 2. Hence, in any equiibrium we are interested in, (MD) The manager gathers information, chooses ψ 1 and induces work from the worker in θ 1, and induces shirk in θ 2. Note that (MD) is the first-best outcome which is not impementabe under centraization. If manager deegation can impement (MD), the arger tota surpus of the first-best outcome is the benefit of deegation. However the owner may not prefer deegation to centraization even if the first-best outcome is possibe under the former. This is because she may have to eave too arge a rent to the manager to induce the desirabe action. Deegation therefore entais both costs and benefits to the owner. The centra aim of this paper is to deineate when such benefits outweigh costs, in which case meaningfu deegation wi emerge endogenousy. Given that the owner has a fina say in the choice of mechanism, we coud view such endogenous deegation as an incentive-based expanation of transition from persona capitaism to manageria capitaism. We now turn to the subcontracting game between the manager and the worker. Denote the manager s contract by σ and the worker s contract by ω i 0 for i = 1, 2, which is a payment for success when ψ i is chosen. Consistent with our assumption, the contact cannot be directy dependent on the manager s private information. When offering a contract to the worker, however, the manager may have acquired information. Thus the manager can design the worker s contract indirecty contingent on his private information. That is, the worker s contract can be designed to signa the manager s information: given ω i, the worker decides on his action based on an inference on the manager s information on the state. Denote this beief by µ(θ ψ i, ω i ), i = 1, 2. 14

17 The equiibrium eading to outcome (MD) is described in more detai as foows: the owner contracts with the manager paying σ 0 in case of success; the manager accepts the contract and incurs c to gather information; if θ 1 is observed, he chooses ψ 1 and offers the worker ω 1 0 in case of success, which the worker accepts and chooses to work; if θ 2 is observed, the manager chooses ψ 2 and offers the worker ω 2 0 in case of success, 14 which the worker accepts and does not exert effort. Beow we check the conditions for such a strategy profie to indeed constitute an equiibrium. Since the owest wage to induce shirk is ceary 0, ω 2 = 0 in equiibrium. When ω 1 is offered, the worker correcty infers θ 1, hence he woud work as ong as ω 1 p 1. [3] Given ω 1 satisfying [3], the worker s equiibrium strategy is work if and ony if ω 1 p 1 when ψ 1 is chosen, and work if and ony if ω 2 q 2 when ψ 2 is chosen. The worker s beief supporting the above strategy is µ(θ 1 ψ 1, ω 1 ) = 1 for ω 1 p 1 and 0 otherwise, and µ(θ 2 ψ 2, ω 2 ) = 1 for a ω 2 > The manager s equiibrium expected payoff is then V 1 πp 1 (σ ω 1 ) + (1 π)rσ c. [4] To check the manager s incentive compatibiity (IC), we consider possibe deviations by the manager. Once he gathers information, no deviation is profitabe in θ 2 as expained earier. In θ 1, he woud get rσ regardess of the project if he induced shirk from the worker; choosing ψ 1 and offering ω 1 is best as ong as he induces work. Hence, the manager s IC after he gathered information is p 1 (σ ω 1 ) rσ. [5] If he does not gather information, he is best off either by choosing ψ 1 and offering ω 1 that satisfies [3] (i.e., inducing work) or by taking either project and offering 0. The conditions for neither to be profitabe are V 1 (πp 1 + (1 π)p 2 )(σ ω 1 ) (1 π)(rσ p 2 (σ ω 1 )) c [6] 14 If the worker is induced to shirk, then project choice does not matter. We assume in this case that the manager chooses ψ 2 because it renders the equiibrium more stabe. 15 We focus on pure strategies of the worker ony since the worker woud accept any positive wage offer because nonnegative payoff is guaranteed by shirking. 15

18 and V 1 rσ π(p 1 (σ ω 1 ) rσ) c. [7] Since [7] impies [5], the manager s IC is summarized by [6] and [7]. In the (ω 1, σ)-space, [6] is satisfied in the area beow a positivey soped straight ine, and [7] is satisfied in the area above a fatter (yet, positivey soped) straight ine. It is straightforward to verify that the vaue of ω 1 at the intersection of these two ines is given by ω c ( p 1 r(p 1 p 2 ) 1 π + p ) 2. [8] π Together with the worker s IC condition [3], we deduce that if ω which is equivaent to c p 1[π p 1 +(1 π) p 2 ] π(1 π)(p 1 p 2 )r be impemented east costy for the owner when ω 1 = p 1, then the outcome (MD) can and σ = 1 ( c p 1 p 1 π + p 1 ) [9] p 1 where σ in [9] is the smaest vaue of σ that satisfies [6] and [7] when ω 1 = p 1. If ω > p 1, then the outcome (MD) can be impemented east costy for the owner at the intersection of [6] and [7], i.e., when ω 1 = ω and σ = 1 ( c p 1 π + cp ( 1 p 1 r(p 1 p 2 ) 1 π + p ) ) 2. [10] π In either case, the owner s expected payoff is Z D (πp 1 + (1 π)r)(x σ). [11] Proposition 4: (a) If ω p 1, then the owner can impement (MD) at minimum cost by offering the manager σ = 1 p 1 ( c + p 1 π p 1 ) in case of success. The optima subcontract the manager offers the worker is ω 1 = p 1 and ω 2 = 0. (b) If ω > p 1, then the owner can impement (MD) at minimum cost by offering the manager σ in [10] in case of success. The optima subcontract the manager offers the worker is ω 1 = ω in [8] and ω 2 = 0. 16

19 5. Centraization vs. Manager Deegation In this section we compare manager deegation and centraization, and anayze when the owner can benefit from deegating authority to the manager. For non-vacuous comparison, we assume that x is arge enough so that the saary needed to induce (MD) in Proposition 4 is ess than x. The owner s expected payoff depends on whether or not the inequaity ω p 1 hods. We focus on the case where the inequaity hods, 16 whence the owner s expected payoff is Z D (πp 1 + (1 π)r) ( x c p ) 1. [12] π p 1 ( p 1 ) 2 We compare Z D with the owner s expected payoffs from centraization and proprietorship, Z C and Z P. Let us start with a numerica exampe where parameter vaues are: p 1 = 0.9, p 2 = 0.3, q 1 = 0.4, q 2 = 0.45, π = 0.63, r = 0.25, = 4, c = 0.1, x = 20. These vaues satisfy Assumptions 1, 2 and ω p 1. The owner s equiibrium expected payoffs are cacuated as Z C = 7.22, Z P = 5, Z D = 7.41, verifying that the owner is better off under manager deegation by impementing (MD). To see how manager deegation performs reative to centraization, we pot how the owner s expected payoffs change as c, and π change. The changes in these parameter vaues are a restricted to the range consistent with our assumptions. 17 Figure 2.1 shows how the owner s equiibrium expected payoffs change when c changes from 0.01 to As c increases, Z D decreases whie Z C and Z P are independent of c. Thus the owner is better off under manager deegation for ower vaues of c. In Figure 2.2, the owner s equiibrium expected payoffs are potted against as changes from 4 to 7.8. As increases, both Z D and Z C decrease but Z D decreases at a smaer rate. At ow vaues of, the owner prefers centraization to manager deegation. As increases, manager deegation dominates centraization unti it is eventuay dominated by proprietorship. Finay, Figure 2.3 shows how the owner s 16 The other case is anaogous but the agebra is much messier. The detais are avaiabe upon request from the authors. 17 In the exampes of Figures 2.2 and 2.3, the vaue of c is set at 0.28, which makes Z C arger than Z D at the start in Figure 2.2, and Z P arger than Z D at the start in Figure

20 equiibrium expected payoffs change as π changes from 0.3 to 0.8. Again manager deegation dominates centraization and proprietorship for intermediate vaues of π. But it is dominated by proprietorship for sma vaues of π, and by centraization for arge vaues of π. The patterns in which the optima form of organizationa structure changes in these figures are indeed genera as discussed beow. Figure 2 goes about here. Consider c first, the manager s cost of information gathering. From the above exampe, we know that there is a set of parameter vaues for which Z D = max{z C, Z P }. Denote such vaue of c by ĉ. 18 Let us now fix a other parameter vaues but change c. Since Z C and Z P are independent of c, and Z D decreases in c, Z D is the argest for a c < ĉ. As c increases beyond ĉ, either Z C or Z P is arger than Z D. This is intuitivey cear because higher c means higher cost of inducing the manager to gather information under manager deegation. Under centraization and proprietorship, the manager is not compensated because he pays no roe. This eads to Proposition 5: Fix a set of parameter vaues and the vaue of c denoted by ĉ for which Z D = max{z C, Z P }. Then Z D max{z C, Z P } for a c ĉ, and Z D max{z C, Z P } for a c ĉ. The next is, the cost of work for the worker. Reca that centraization resuts in suboptima incentives for the worker since the owner does not have access to the manager s information. That is, the worker works in θ 2 even if his margina product is ess than the cost of work. An increase in then magnifies this inefficiency of centraization. Whie an increase in aso increases the cost of the manager s compensation under deegation, the deegated manager uses his information to correct the inefficient work incentives for the worker. Indeed it is easy to see that the worker is stricty worse off under manager deegation than under centraization. 19 On baance, the inefficiency of centraization is more pronounced than the increase in the compensation cost as increases, which is shown in the proof of the foowing proposition. Therefore we expect centraization to dominate manager 18 In Figure 2.1, the approximate vaue of ĉ is Denoting the worker s equiibrium expected payoffs by U C and U D under centraization r and deegation respectivey, one can show that U C U D = π p 1+(1 π) p 2 πr p 1 > 0. 18

21 deegation for sma vaues of, which is reversed when becomes arge. However, if becomes sufficienty arge, then proprietorship dominates both organizationa structures because both Z C and Z D decrease in whie Z P is independent of. 20 Summarizing, we have Proposition 6: Fix a set of parameter vaues and the vaue of denoted by 1 for which Z D = Z C > Z P. Then there is a nonempty interva ( 1, 2 ) such that Z D < Z C for a < 1, Z D max{z C, Z P } for a [ 1, 2 ], and Z D < Z P for a > 2. Proof: See the appendix. Finay consider π, the prior probabiity of state θ 1. The vaue of the manager s information is its use in identifying the different states, based on which to choose a project and provide proper incentives to the worker. Therefore the manager s information does not have much vaue when π becomes too arge or too sma. If π is so sma that inducing shirk is amost certainy optima, then the owner is best off with proprietorship. Simiary, if π is so arge that seecting ψ 1 and inducing work is amost certainy optima, then the owner is best off with centraization without the manager s information. It then foows that deegation can be optima for intermediate vaues of π. In this case, the manager s information is vauabe since uninformed decisions carry a arge risk. It can be shown that the set of vaues of π for which Z D is arger than Z C and Z P given other parameter vaues, is convex. 21 Proposition 7: Fix a set of parameter vaues and the vaue of π denoted by ˆπ for which Z D = Z C > Z P. Then there is a nonempty interva of π with ˆπ as an endpoint, on which Z D max{z C, Z P } with strict inequaity in the interior of the interva. Moreover, there is an interva [0, π 1 ] with π 1 < ˆπ where Z P > max{z C, Z D }, and an interva [π 1, 1] with π 2 > ˆπ where Z D < Z C Proof: See the appendix. We summarize the main findings of this section. Under centraization, the owner is unabe to motivate the manager to gather information. As 20 In Figure 2.2, the approximate vaue of is when Z D = Z C, and when Z D = Z P. 21 In Figure 2.3, this interva is approximatey given by [0.363, 0.617]. 19

22 a resut, she makes a suboptima project choice, and the ensuing contract for the worker eaves the worker too much rent. If the deegated manager gathers information, then project choice is optima and the worker s rent can be reduced. Choosing manager deegation instead of centraization, the owner thus trades off the benefits of better information and ower incentive cost for the worker against the compensation cost for the manager. The benefits of deegation increase as the manager s information becomes more vauabe and the worker needs to be compensated more for his effort. On the other hand, the cost of manager deegation increases as it becomes more costy for the manager to gather information. As a consequence, manager deegation is more ikey to dominate centraization if the manager s cost of information gathering is smaer, the worker s cost of work is arger, and the manager s information becomes more vauabe. 6. Further Discussions and Extensions 6.1. Aternative contracting under centraization Under centraization, we assumed that the owner designs the worker s contract after receiving the manager s report and making a project choice. This resuted in the impossibiity of an equiibrium in which the manager gathers information. The reason for this is stringent incentive compatibiity constraints for the manager. Since the manager knows that his information wi be used (indirecty through project choice) in contract design for the worker, which in turn affects his expected payoff, he is tempted to make a fase report to induce the worker to work even though it may not be optima for the owner. The stringent incentive compatibiity constraints for the manager increase the cost of using the manager s information for the owner, which is not in her interest. Consider now an aternative timing of contracting in which the owner simutaneousy offers contracts to both agents before receiving the manager s report and making a project choice. Furthermore, suppose that the owner uses contracts that are based on the fina return ony. Since the owner uses ony return-based contracts without the manager s information, she cannot induce different work decisions from the worker in different states: the worker 20

23 is induced to work in both states or shirk in both states. 22 In this case, the manager s information does not have the indirect effect of affecting the worker s action. Thus it is easier to eicit truth-teing from the manager compared to centraization in our main mode. Then it is possibe to show that there is an equiibrium where the manager gathers information and reports it truthfuy. Proposition 8: Suppose the owner designs contracts based ony on the fina return from the project before receiving the manager s report. Then an equiibrium exists in which the manager gathers and truthfuy reports information, the project choice is C(θ i ) = ψ i, i = 1, 2, and the worker works in both states. Proof: See the appendix. The main reason for the above resut is that the manager s report cannot affect the worker s action via the worker s contract. This reduces the manager s incentive to manipuate information, thereby reaxing his incentive compatibiity constraints. This aternative contracting can thus ameiorate the manager s incentive probem in the presence of interocking incentives Worker deegation The anayses of the previous sections indicate that manager deegation can benefit the owner ony when deegation impements the outcome that the owner coud not impement under centraization. Then, can the owner benefit by deegating authority to the worker instead? Specificay, the game under worker deegation proceeds as: the owner offers the worker a contract; the worker offers the manager a contract; the manager decides on information gathering and makes a report to the worker; the worker chooses a project and makes his effort decision. In this new game, the worker faces the same probem as the owner under centraization when offering a contract to the manager. Since the worker s effort decision foows the manager s report, the manager sti has incentives to make a fase report to induce work from the worker. As in centraization, this makes it impossibe for the worker to induce 22 The timing of contracting is aso crucia. If the owner offers the worker a contract after receiving the manager s report and making a project choice, then she can induce different work decisions from the worker even using return-based contracts. 21

24 the manager to gather information. Consequenty, worker deegation cannot impement an outcome that cannot be impemented under centraization. The worker makes a project choice and decides on his effort without the manager s information, which the owner can repicate under centraization. Proposition 9: The owner is never better off under worker deegation than under centraization. Proof: See the appendix Extension to p 1 > q 2 > x In this section we consider the case that Assumption 2 is reaxed as p 1 > q 2 >. Proposition 3 sti hods. Reative to the previous case, x the foowing outcome can be optima now: (MD2) The manager gathers information, the project choice is ψ i in state θ i, i = 1, 2, and the worker works in both states. This outcome may be impementabe under centraization as we as under deegation. In fact, if the manager gathers information under centraization, this is the equiibrium outcome: in the proof of Proposition 1, Assumption 2 is used ony to eiminate (MD2). We show beow that if (MD2) is impementabe under centraization, it can be done at no higher cost for the owner than under deegation. Therefore, deegation may be preferred by the owner ony if it can impement an outcome, (MD) or (MD2), that cannot be impemented under centraization. That is, the benefits of deegation come from circumventing the irreconciabe conficts between the information hoder and the decision maker, which may arise under centraization, preventing a certain outcome from being impementabe. The benefits do not stem from more economica impementation of the same outcome: even though the worker s incentives can be provided more efficienty under deegation, it comes at the additiona cost of motivating the manager. Proposition 10: Suppose p 1 > q 2 >. If (MD2) is impementabe x under both centraization and deegation, then the owner weaky prefers to impement it under centraization. Proof: See the appendix. 22